\(A=1-\frac{1}{1-\frac{2}{1-\frac{3}{1-\frac{1}{4}}}}\)
làm giúp mk nhanh nhất sẽ đc 3 tick( nhanh nha gấp lắm rồi)
K
Khách
Hãy nhập câu hỏi của bạn vào đây, nếu là tài khoản VIP, bạn sẽ được ưu tiên trả lời.
Những câu hỏi liên quan
30 tháng 3 2016
A = 1/ 12 +1/22+1/32+. . . +1/502 < 1+ 1/1.2 + 1/2.3 + 1/3.4 + 1/4.5+ . . . + 1/49.50
<=> A < 1 + 1 - 1/2 + 1/2 - 1/3 + 1/3 - 1/4 +. . . + 1/49 - 1/50
<=> A< 1 + 1 - 1/50 = 2 - 1/50
Vậy A < 2
Nhớ k nhé bạn ^^
N
1 tháng 8 2019
1.
a) \(\frac{11}{2}-\frac{2}{3}:\left|2x+-\frac{3}{2}\right|=3\)
\(-\frac{2}{3}:\left|2x+-\frac{3}{2}\right|=3-\frac{11}{2}\)
\(-\frac{2}{3}:\left|2x+-\frac{3}{2}\right|=-\frac{5}{2}\)
\(\left|2x+-\frac{3}{2}\right|=-\frac{2}{3}:\left(-\frac{5}{2}\right)\)
\(\left|2x+-\frac{3}{2}\right|=\frac{4}{15}\)
\(\Rightarrow\left|2x+-\frac{3}{2}\right|\in\text{{}\frac{4}{15};-\frac{4}{15}\)}
Nếu, \(2x+\left(-\frac{3}{2}\right)=\frac{4}{15}\)
\(2x=\frac{53}{30}\)
\(x=\frac{53}{60}\)
Nếu, \(2x+\left(-\frac{3}{2}\right)=-\frac{4}{15}\)
\(2x=\frac{37}{30}\)
\(x=\frac{37}{60}\)
Vậy \(x\in\text{{}\frac{53}{60};\frac{37}{60}\)}
b) \(\left|\frac{2}{7}x-\frac{1}{5}\right|-\left|-x+\frac{4}{9}\right|=0\)
\(\left|\frac{2}{7}x-\frac{1}{5}\right|=\left|-x+\frac{4}{9}\right|\)
\(\Rightarrow\left|\frac{2}{7}x-\frac{1}{5}\right|\in\text{{}-x+\frac{4}{9};-\left(x+\frac{4}{9}\right)\)}
Nếu, \(\frac{2}{7}x-\frac{1}{5}=-x+\frac{4}{9}\)
\(x=\frac{203}{405}\)
Nếu, \(\frac{2}{7}x-\frac{1}{5}=-\left(-x+\frac{4}{9}\right)\)
\(\frac{2}{7}x-\frac{1}{5}=x-\frac{4}{9}\)
\(\frac{2}{7}x-x=\frac{1}{5}-\frac{4}{9}\)
\(-\frac{5}{7}x=-\frac{11}{45}\)
\(x=\frac{77}{225}\)
Vậy \(x\in\text{{}\frac{203}{405};\frac{77}{225}\)}
23 tháng 4 2019
Đặt \(A=\frac{1}{31}+\frac{1}{32}+...+\frac{1}{90}\)
\(=\left(\frac{1}{31}+\frac{1}{32}+...+\frac{1}{45}\right)+\left(\frac{1}{46}+\frac{1}{47}+...+\frac{1}{90}\right)\)
Đặt \(B=\frac{1}{31}+\frac{1}{32}+...+\frac{1}{45}\)
Ta có: \(\frac{1}{31}>\frac{1}{45}\)
\(\frac{1}{32}>\frac{1}{45}\)
....................
\(\frac{1}{45}=\frac{1}{45}\)
\(\Rightarrow B>\frac{1}{45}.15\)
\(\Rightarrow B>\frac{1}{3}\)
Đặt \(C=\frac{1}{46}+\frac{1}{47}+...+\frac{1}{90}\)
Ta có: \(\frac{1}{46}>\frac{1}{90}\)
\(\frac{1}{47}>\frac{1}{90}\)
.....................
\(\frac{1}{90}=\frac{1}{90}\)
\(\Rightarrow C>\frac{1}{90}.45\)
\(\Rightarrow C>\frac{1}{2}\)
\(\Rightarrow B+C>\frac{1}{3}+\frac{1}{2}\)
Hay \(A>\frac{5}{6}\left(1\right)\)
Lại có: \(A=\left(\frac{1}{31}+...+\frac{1}{59}\right)+\left(\frac{1}{60}+...+\frac{1}{90}\right)\)
Đặt \(D=\frac{1}{31}+...+\frac{1}{59}\)
Ta có: \(\frac{1}{31}< \frac{1}{30}\)
. ...................
\(\frac{1}{59}< \frac{1}{30}\)
\(\Rightarrow D< \frac{1}{30}.60\)
\(\Rightarrow D< \frac{1}{2}\)
Đăt \(E=\frac{1}{60}+...+\frac{1}{90}\)
Ta có: \(\frac{1}{60}=\frac{1}{60}\)
.................
\(\frac{1}{90}< \frac{1}{60}\)
\(\Rightarrow E< \frac{1}{60}.31\)
\(\Rightarrow E< \frac{31}{60}< 1\)
\(\Rightarrow E< 1\)
\(\Rightarrow E+D< 1+\frac{1}{2}\)
Hay \(A< \frac{3}{2}\left(2\right)\)
Từ (1) và (2) \(\Rightarrow\frac{5}{6}< A< \frac{3}{2}\)
13 tháng 8 2019
Xét dạng tổng quát :
\(\sqrt{1+\frac{1}{k^2}+\frac{1}{\left(k+1\right)^2}}=\sqrt{\frac{k^2+1}{k^2}+\frac{1}{\left(k+1\right)^2}}\)
\(=\sqrt{\frac{\left(k^2+1\right)\left(k+1\right)^2+k^2}{k^2\left(k+1\right)^2}}=\sqrt{\frac{k^4+2k^3+3k^2+2k+1}{k^2\left(k+1\right)^2}}\)
\(=\sqrt{\frac{\left(k^2+k+1\right)^2}{k^2\left(k+1\right)^2}}=\frac{k^2+k+1}{k\left(k+1\right)}=1+\frac{1}{k\left(k+1\right)}=1+\frac{1}{k}-\frac{1}{k+1}\)
Áp dụng vào bài toán :
\(A=\sqrt{1+\frac{1}{2^2}+\frac{1}{3^2}}+\sqrt{1+\frac{1}{3^2}+\frac{1}{4^2}}+...+\sqrt{1+\frac{1}{2010^2}+\frac{1}{2011^2}}\)
\(A=1+\frac{1}{2}-\frac{1}{3}+1+\frac{1}{3}-\frac{1}{4}+...+1+\frac{1}{2010}-\frac{1}{2011}\)
\(A=2009-\frac{1}{2011}+\frac{1}{2}\)
p/s: không biết tính có đúng ko nữa, bạn nhớ check lại. Mình nhớ bài này còn có cách khác ngắn hơn nhưng quên rồi :D
23 tháng 6 2017
1/3xD=1/(2x4)+1/(4x6)+...+1/(98x100)
2/3xD=2/(2x4)+2/(4x6)+...+1/(98x100)
2/3xD= 1/2-1/4+1/4-1/6+...+1/98-1/100
2/3xD=1/2-1/100
2/3xD=49/100
D=147/200
LV
20 tháng 3 2016
a)\(\frac{32}{64}-\frac{16}{64}+\frac{8}{64}-\frac{4}{64}+\frac{2}{64}-\frac{1}{64}\le\frac{1}{3}\)
\(\Rightarrow\frac{32-16+8-4+2-1}{64}=\frac{23}{64}\)\
\(\Rightarrow\frac{23}{64}=0,359375;\frac{1}{3}=0,33333...\)
đề sao lạ vậy
D
22 tháng 4 2017
Ta có: \(1\frac{4}{5}+2\frac{5}{7}+3\frac{4}{5}+4\frac{5}{7}\)
\(=\left(1\frac{4}{5}+3\frac{4}{5}\right)+\left(2\frac{5}{7}+4\frac{5}{7}\right)\)
\(=\left(\frac{9}{5}+\frac{19}{5}\right)+\left(\frac{19}{7}+\frac{33}{7}\right)\)
\(=\frac{28}{5}+\frac{52}{7}=13\frac{1}{35}\)
22 tháng 4 2017
= ( \(1\frac{4}{5}\)+ \(3\frac{4}{5}\)) + ( \(2\frac{5}{7}\)+ \(4\frac{5}{7}\))
= \(4\frac{4}{5}\) + \(6\frac{5}{7}\)
= \(\frac{24}{5}\) + \(\frac{47}{7}\)
= ...... ( tính nốt nhé )
\(\frac{1}{1-\frac{2}{1-\frac{3}{1-\frac{1}{4}}}}=\frac{1}{1-\frac{2}{1-\frac{3}{\frac{3}{4}}}}=\frac{1}{1-\frac{2}{1-4}}=\frac{1}{1-\frac{2}{-3}}=\frac{1}{\frac{5}{3}}=\frac{3}{5}\Rightarrow A=1-\frac{3}{5}=\frac{2}{5}\)
Bài làm
\(A=1-\frac{1}{1-\frac{2}{1-\frac{3}{1-\frac{1}{4}}}}\)
\(A=1-\frac{1}{1-\frac{2}{1-\frac{3}{\frac{4}{4}-\frac{1}{4}}}}\)
\(A=1-\frac{1}{1-\frac{2}{1-\frac{3}{\frac{3}{4}}}}\)
\(A=1-\frac{1}{1-\frac{2}{1-3:\frac{3}{4}}}\)
\(A=1-\frac{1}{1-\frac{2}{1-4}}\)
\(A=1-\frac{1}{1-\frac{2}{-3}}\)
\(A=1-\frac{1}{1+\frac{2}{3}}\)
\(A=1-\frac{1}{\frac{3}{3}+\frac{2}{3}}\)
\(A=1-\frac{1}{\frac{5}{3}}\)
\(A=1-1:\frac{5}{3}\)
\(A=1-\frac{3}{5}\)
\(A=\frac{5}{5}-\frac{3}{5}\)
\(A=\frac{2}{5}\)
Vậy \(A=\frac{2}{5}\)
# Học tốt #